Skyrme Sphalerons of anO(3)-σ Model and the Calculation of Transition Rates at Finite Temperature

Abstract

The reduced O(3)‐σ model with an O(3)‐σ→ O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i.e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the flucuation path integrals which is therefore evaluated using a measuremodified Fourier‐Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme‐less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.

Quantum-classical crossover for the biaxial spin model with field applied along the hard axis

“…For common metastable or double-well potentials, such as cubic or quartic parabolas, the second-order crossover is realized. Examples of systems and processes showing firstorder crossover include superconducting quantum interference devices with two Josephson junctions [2], false vacuum decay in field theories [3][4][5][6], depinning of a massive string from a linear defect [7], and depinning of flux lines from columnar defects [8]. In the last few years, another process has drawn much attention: quantum-classical crossover in the rate of escape of a spin system out of a metastable well [9][10][11][12][13][14][15][16][17].…”